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A308081 Index positions of the points of a counterclockwise square spiral as described by A174344 and A274923 in a list of points with integer coordinates with primary sorting by radius and secondary sorting by polar angle as given by A305575 and A305576.

%I A308081 #10 May 12 2019 15:13:01
%S A308081 0,1,5,2,6,3,7,4,8,20,9,13,21,14,10,15,22,16,11,17,23,18,12,19,24,44,
%T A308081 36,25,29,37,57,38,30,26,31,39,58,40,32,27,33,41,59,42,34,28,35,43,60,
%U A308081 80,68,56,45,49,61,70,97,71,62,50,46,51,63,73,98,74,64
%N A308081 Index positions of the points of a counterclockwise square spiral as described by A174344 and A274923 in a list of points with integer coordinates with primary sorting by radius and secondary sorting by polar angle as given by A305575 and A305576.
%C A308081 The sequence is a permutation of the integers.
%H A308081 Hugo Pfoertner, <a href="/A308081/b308081.txt">Table of n, a(n) for n = 1..10000</a>
%o A308081 (PARI) /* It is assumed that the files a305575 and a305576 contain the second column of the corresponding b-files omitting the initial 0 */
%o A308081 a305575=readvec(a305575); a305576=readvec(a305576);
%o A308081 a174344=vector(10000); L=0; d=1; n=0;
%o A308081 for(r=1, 100, d=-d; k=floor(r/2)*d; for(j=1, L++, a174344[n++]=k); forstep(j=k-d, -floor((r+1)/2)*d+d, -d, a174344[n++]=j));
%o A308081 a274923=vector(10100); L=1; d=1; n=0;
%o A308081 for(r=1, 100, d=-d; k=floor(r/2)*d; for(j=1, L++, a274923[n++]=k); forstep(j=k-d, -floor((r+1)/2)*d+d, -d, a274923[n++]=j));
%o A308081 findinring(i, j)={my(s=i*i+j*j);if(s==0,return(0),forstep(k=floor(Pi*(s+1))+sqrtint(s),1,-1,if(i==a305575[k]&&j==a305576[k], return(k))))};
%o A308081 for(n=1,67,print1(findinring(a174344[n],a274923[n]),", "));
%Y A308081 Cf. A174344, A274923, A305575, A305576, A308080.
%K A308081 nonn
%O A308081 1,3
%A A308081 _Hugo Pfoertner_, May 11 2019